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Pierre J.P. Pimienta and Edward J. Garboczi
Building Materials Division
W. Craig Carter
Ceramics Division
National Institute of Standards and Technology
Gaithersburg, MD 20899
Abstract
A cellular automaton algorithm is developed that simulates the evolution of a surface due to
surface mass transport. The driving force is the reduction of chemical potential differences on the
surface. This process is important in the development of microstructure during the sintering of
powders. The algorithm is implemented in 2d in a digital image mode, using discrete pixels to
represent continuum objects. The heart of the algorithm is a pixel-counting-based method for
computing the potential at a pixel located in a digital surface. This method gives an approximate
measure of the curvature at the given surface pixel. The continuum version of this method is
analytically shown to give the true curvature at a point on a continuum surface. The digital
version of the curvature computation method is shown to obey the scaling laws derived for the
continuum version. Several examples, both quantitative and qualitative, are computed of surfaces
evolving under curvature differences, and are shown to agree with the known physics of sintering.